Question

Тригонометрия. Решить уравнение.

Answer 1

d=21^2-4*10*2=361
sin(x)=(21+19)/4 - ложный корень
sin(x)=(21-19)/4=0,5
x1=pi/6+2*pi*k
x2=5pi/6+2*pi*n

Answer 2

Trigonometry and Solving Equations

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. It is widely used in various fields, including physics, engineering, and navigation. Solving trigonometric equations involves finding the values of the variables that satisfy the given equation.

Here are a few examples of solving trigonometric equations:

1. Example 1: Solving for cos(x) = 0.9 - The solutions for this equation can be found using the inverse cosine function. - The general solution is given by \(x = \pm \arccos(0.9) + 2\pi k\), where \(k\) is an integer.

2. Example 2: Solving for sin(x) = 0 - The solutions for this equation can be found using the inverse sine function. - The general solution is given by \(x = n\pi\), where \(n\) is an integer.

3. Example 3: Solving a more complex trigonometric equation - Consider the equation \(2\sin^2(x) + \sin(x) = 0\) with the constraint \(2\cos(x) - \sqrt{3} \neq 0\). - To solve this equation, we can set up a system of equations: - \(2\sin^2(x) + \sin(x) = 0\) - \(2\cos(x) - \sqrt{3} \neq 0\) - The solutions for the first equation are given by \(x = n\pi\) or \(x = \arcsin(0)\).

Please note that these are just a few examples of solving trigonometric equations. There are many other types of equations and methods for solving them in trigonometry.

Let me know if there's anything else I can help you with!